Particle-in-Cell (PIC) simulation is the most important numerical tool in plasma physics. However, its long-term accuracy has not been established. To overcome this difficulty, we developed a canonical symplectic PIC method for the Vlasov-Maxwell system by discretizing its canonical Poisson bracket. A fast local algorithm to solve the symplectic implicit time advance is discovered without root searching or global matrix inversion, enabling applications of the proposed method to very large-scale plasma simulations with many, e.g., 10 9 , degrees of freedom. The long-term accuracy and fidelity of the algorithm enables us to numerically confirm Mouhot and Villani's theory and conjecture on nonlinear Landau damping over several orders of magnitude using the PIC method, and to calculate the nonlinear evolution of the reflectivity during the mode conversion process from extraordinary waves to Bernstein waves.

Secular dynamics of relativistic charged particles has theoretical significance and a wide range of applications. However, conventional algorithms are not applicable to this problem due to the coherent accumulation of numerical errors. To overcome this difficulty, we develop a volumepreserving algorithm (VPA) with long-term accuracy and conservativeness via a systematic splitting method. Applied to the simulation of runaway electrons with a time-span over 10 magnitudes, the VPA generates accurate results and enables the discovery of new physics for secular runaway dynamics. V C 2015 AIP Publishing LLC. [http://dx.

It is discovered that the tokamak field geometry generates a pitch-angle scattering effect for runaway electrons. This neoclassical pitch-angle scattering is much stronger than the collisional scattering and invalidates the gyro-center model for runaway electrons. As a result, the energy limit of runaway electrons is found to be larger than the prediction of the gyro-center model and to depend heavily on the background magnetic field.

La-doped BiFeO 3 thin films with Fe 2+ ions have been prepared on Pt/ TiO 2 / SiO 2 / Si substrates by pulsed laser deposition in order to enhance the ferroelectric and magnetic properties. The targets for the film deposition were synthesized using a rapid liquid phase sintering technique to ensure the low leakage. The dielectric properties at room temperature and above were investigated. It was observed that the La doping greatly enhances the ferroelectric polarization at room temperature by modifying the film structure from rhombohedral to monoclinic. The saturation magnetization was enhanced about two times due to the Fe 2+ ions in the thin films.